"The child is experiencing significant difficulties in acquiring literacy and numeracy skills compared to his peers despite having had access to appropriate learning opportunities."
All this tells you is that the child is not progressing as fast as peers. It doesn't tell you if the rate has slowed, stayed the same or increased following 'appropriate learning opportunities' and it doesn't tell you if 'appropriate learning opportunities are a) the same opportunities as all children have b) some extra help c) specialised input and resources.
So, this sentence isn't very clear. You could have 3 different children that the phrase applies to, with very different outcomes:
"Tom is experiencing significant difficulties in acquiring literacy and numeracy skills compared to his peers despite having had access to appropriate learning opportunities. Since the start of Year 4, all children have been given the same tuition. Tom's peers have progressed 2 sub levels on average, whereas Tom's progress is static."
The LA might say 'well, the school needs to move Tom onto School Action and give extra support.'
"Dick is experiencing significant difficulties in acquiring literacy and numeracy skills compared to his peers despite having had access to appropriate learning opportunities. Since the start of Year 4, Tom has been given adult support for literacy and the use of a scribe. Despite this, his progress has been much slower than that of his peers and has not increased despite this intervention."
The LA might say 'well Dick needs to be given Reading recovery, etc., and given consistent adult support.'
"Harry is experiencing significant difficulties in acquiring literacy and numeracy skills compared to his peers despite having had access to appropriate learning opportunities. Since the start of Year 4, Harry has had 1:1 support, Reading recovery, outside agency x has been involved and pen grips, sloping writing boards used, etc......He has made no progress at all."
The LA might say 'Ok, Harry has been given all the resources that the school should be expected to offer. Harry needs a statement.'
Those aren't very realistic scenarios, but it starts to give you an idea about how wooly those phrases are.